Leading figures from the yachting world have joined more than 100,000 people who have signed an online petition calling on US authorities to resume the search for four British sailors who went missing after their yacht capsized in the Atlantic Ocean.

Health Secretary Jeremy Hunt, the local MP for one of the missing men, has appealed to the US Coast Guard (USCG) not to give up and entrepreneur and adventurer Sir Richard Branson has called on vessels near the area to keep a lookout.

However, the Government said discussions with the US have shown that the USCG believes it has done everything it can to find the sailors alive.

The crew of the 40ft (12m) Cheeki Rafiki ran into difficulties about 620 miles (998km) east of Cape Cod in Massachusetts last Thursday while returning to the UK from a regatta in Antigua. Contact with the yacht was lost in the early hours of Friday when they diverted to the Azores.

The coastguard, Canadian aircraft and three merchant vessels searched for them throughout Friday and Saturday but called off efforts on Sunday at 5am local time amid treacherous weather.

Relatives of the four men - experienced captain Andrew Bridge, 22, and crew members James Male, 23, Steve Warren, 52, and Paul Goslin, 56 - have pleaded with the US Coast Guard to resume the search and remain convinced that their loved ones are alive.

Dame Ellen MacArthur, who twice broke the world record for fastest solo circumnavigation of the globe, said there was "every chance" that the sailors were still alive.

She said: " It seems that there is an element of everyone working in the dark here as the incident happened so far from land and there is no longer contact with the crew. However there is every chance that the sailors could be alive either inside the hull of the vessel, or in the life-raft which is designed to keep people alive at sea.

"There are examples of both types of survival, and in both cases for extended periods of time."

And Dee Caffari, who completed the Vendee Globe solo non-stop round-the-world yacht race, is currently training with Team SCA for the Volvo Ocean Race later this year, and is assisting with the Marine Rescue Co-ordination Centre (MRCC) at Falmouth.

Her partner, Harry Spedding, said: "They are expecting to pass through the search area and they have been in contact with the search authorities and co-ordinating with the MRCC.

"It is quite emotive for them but there is not a lot that they can do because of the conditions at the moment and, from a yacht, the search horizon, if you are lucky, is only three miles."

Mike Golding, who is one of the few yachtsmen to have sailed around the world non-stop in both directions, said the US Coastguard said that a further search was needed, especially to locate the hull and establish whether a life raft had been released.

He said: "It's hard to imagine four men, well-equipped, even with a boat in trouble actually disappearing like that.

"The boat had all the right safety equipment, people are just saying the search period was very short. "

Some 4,000 square miles (10,360 sq km) were scanned for the "very well-equipped" vessel's two personal location GPS beacons until no more transmissions were received from the small devices, which have a short battery life.

On Saturday, a cargo vessel which was helping with the search spotted and photographed an overturned hull which matched the description of the Cheeki Rafiki but reported no signs of people on board or a life raft.

Mr Golding said: "From the images, the yacht has lost the keel, initially they were sinking, taking on water. One imagines they put out the mayday, prepared themselves for sinking, then the keel fell off, maybe the boat rolled over fast and the question is what happened at that point? Were they able to launch the life raft at that point?"

He added that efforts should be made to locate the hull, which he believed could still be afloat, having lost its heavy keel, to establish whether the life raft was still in place and if the sailors were gathered in an air pocket underneath.

He added: "It's an awful situation. These are clearly four experienced sailors - it's very hard for the family and people who sail to imagine them not being able to save themselves somehow.

"We can completely understand the agony the family must be going through, maybe more can be done.

"The US Coastguard is an extremely professional organisation, they won't have called the search off lightly, but if it were me I would want to know if the life raft was still on the vessel."

Sir Robin Knox-Johnston, the first man to sail single-handedly around the world, told the BBC: "Knowing the US Coastguard, I do feel one's got to listen to them.

"They know more about this than anyone else."

But he added: "Isn't it just worth just one more check, just to make sure?"

However, oceanographer Simon Boxall from University of Southampton, said: "It is highly unlikely, beyond reasonable doubt, that they would have missed a life raft - they are bright red or bright orange.

"And if the people were in a life raft and were aware there were rescue aircraft they would have had distress flares and beacons on board and they would have deployed them."

A Downing Street spokesman said: " We have been in constant touch with the US authorities today and throughout the weekend, including Mark Simmonds, Minister for Consular Affairs, speaking to the head of the US Coast Guard and through our embassy in Washington and our consulate in Boston.

"The USCG have been open and collaborative throughout. They have assured us that they did everything they could, and would have done exactly the same for US citizens. This included an air search of over 20 sorties involving three different aircraft, conducted for twice as long as their standard procedures required, in very difficult and challenging weather conditions.

"Our own Coastguard have been fully briefed throughout and believe the USCG have done everything they could."

Mr Bridge, from Farnham, Surrey, was being paid by Southampton-based yacht training and charter company Stormforce Coaching for his role as captain, a spokeswoman for the firm said.

He had taken part in Antigua Week together with Mr Goslin, from West Camel, Somerset, Mr Warren, from Bridgwater, also in Somerset, and Mr Male, from Southampton, all described as "very experienced offshore yachtsmen".

Mr Hunt, MP for South West Surrey, the constituency in which Mr Bridge lives, tweeted his support for the search to restart.

Sir Richard told the BBC: "There are a lot of yachts, both sailing yachts and motor yachts, that are crossing the Atlantic this time of year and I think if they could just go off course a little bit, keep their eyes open, a lot of merchant ships, that would be great and I think the family would be incredibly grateful."

Mr Goslin's daughter, Claire, wrote on the petition, which has attracted more than 114,000 signatures: "One of the sailors is my dad and we cannot give up! He is my world and we need to start this search again!!!"

Gemma Townsend added: " My uncle is on board. We mustn't give up. Two days searching is not enough. When people have survived many months on life rafts."

Kay Coombes, the sister of Mr Warren, a project manager for an electrical company, said she and their mother, Margaret Warren, were convinced that he was still alive.

The 46-year-old said: "It's an utter nightmare. We are grateful for the US and Canadian coastguards for what they have done so far, but it's stopped too soon after two days, it's not long enough, we believe they are still alive.

"They are four strong-minded, physically strong sailors, they knew they were in difficulties and had every opportunity to get into the life raft which would have had provisions for several days. But if no-one is looking for them, they won't be found."

She added: "Everyone is just trying to put pressure on the US Coast Guard using every channel possible. They said they would only continue the search when any debris was found but if no-one is looking how can they find it? There are only passing ships in a very big ocean."